Locally conformally symplectic deformation of Gromov non-squeezing

We prove one deformation theoretic extension of the Gromov non-squeezing phenomenon to $lcs$ structures, or locally conformally symplectic structures, which suitably generalize both symplectic and contact structures. We also conjecture an analogue in $lcs$ geometry of contact non-squeezing of Eliashberg-Polterovich and discuss other related questions.